We've had basically the same philosophy! I mean, we've made it this far and it's been perfectly fine to just encourage more in-depth work and exploring the world when they're at home. (In the early grades we did a bit of actual, semi-formal school work in their free time, but there's just too much else going on at this point for that to work.) It can be really nice to have the kids so unfazed by or ahead of the coursework that teachers never hesitate to approve a pre-planned absence. "They'll be FINE."
But this year has been a little tougher. I've come to feel that it's okay to expect a little more, to see some interest paid to them as individuals with their own set of challenges. Like you said, they're in hours and hours of school followed by a short burst before bedtime in which to accomplish extracurriculars, sports, and self-directed learning. It's just not enough. Either school has to become more than a placeholder, or we have to keep them home. I would LOVE to delve into homeschool. I am just very reluctant to abandon the public school.
I'm so glad to hear that you've gotten the buy-in from administration to do partial homeschool! I will definitely bring something like that up with the principal. My kids would LOVE that option. The idea is growing on them that if we want something different than school offers, we're going to have to get it done ourselves, but they are really reluctant to leave the school structure and friends and teachers they've come to know.